Reviewed by CalcMulti Editorial Team·Last updated: ·← Geometry Hub
The law of sines states that in any triangle, each side divided by the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). This ratio also equals the diameter of the triangle's circumscribed circle (2R).
Use the law of sines when you know: (1) AAS — two angles and any side, (2) ASA — two angles and the included side, or (3) SSA — two sides and a non-included angle (the ambiguous case, which can give 0, 1, or 2 valid triangles).
For SSS or SAS configurations, use the law of cosines instead. This calculator handles all solvable cases and flags the ambiguous case when two solutions exist.
a / sin(A) = b / sin(B) = c / sin(C)
SSS and SAS triangle solving
Right Triangle CalculatorPythagorean theorem + all sides and angles
Triangle Area CalculatorArea using ½ab·sin(C)
Sector Area CalculatorCircular sector area from radius and angle
Perimeter CalculatorPerimeter of triangles and shapes
Polygon Area CalculatorRegular polygons 3–12 sides
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.